Question

Imagine that you flip two coins at the same time.

​

​Create a probability distribution of all the possible outcomes.

​What is the prediction for the number of times both coins will land on heads?

​

​The prediction is
time.

Answer 1

When flipping two coins, each coin can land either heads (H) or tails (T). The possible outcomes when flipping two coins can be represented as follows:

1. HH (both coins are heads)
2. HT (first coin heads, second coin tails)
3. TH (first coin tails, second coin heads)
4. TT (both coins are tails)

Now, let's create a probability distribution for these outcomes. Assuming the coins are fair, the probability for each outcome is equal. Since there are 4 possible outcomes, each outcome has a probability of:

\[
P(\text{Outcome}) = \frac{1}{4} = 0.25
\]

The probability distribution can be summarized as follows:

| Outcome | Probability |
|---------|-------------|
| HH | 0.25 |
| HT | 0.25 |
| TH | 0.25 |
| TT | 0.25 |

Now, regarding the prediction for the number of times both coins will land on heads, we can use the probabilities.

If you conduct a certain number of trials (e.g., flipping the two coins a certain number of times), you can expect the number of times both coins land on heads (HH) to be:

\[
\text{Expected Count (HH)} = \text{Number of Trials} \times P(HH)
\]

If you have a specific number of trials in mind, you can substitute that value into the equation. For example, if you flip the coins 100 times, you would expect to see both coins land on heads about:

\[
\text{Expected Count (HH)} = 100 \times 0.25 = 25 \text{ times}
\]

Thus, your prediction would be based on the number of times you flip the coins. If you provide a specific number of flips, I can give you an exact prediction.